In many previous works, zeolites are the commercially available adsorbents mostly studied for CO2 capture, with attention to zeolite 5A and zeolite 13X. In this study, we have modelled the adsorption equilibrium and simulated the breakthrough curves for the adsorption of carbon dioxide on Pressure Swing Adsorption (PSA) processes for CO2 capture from a mixture with 15% CO2–85% N2 (simulating dry post-combustion flue gases of a coal-fired power station) using the experimental characterization of zeolite 5A and zeolite 13X published in a recent bibliography. A model based on the Linear Driving Force (LDF) approximation for the mass balance, including energy balance and momentum, was used for the simulation of CO2 capture in pressure swing adsorption systems. The models were described by partial differential equations (PDEs) coupled with Algebraic Equations (PDAEs) including conservation equations, models for equation of state, equilibrium, thermodynamic, and transport properties. This work was implemented and solved with Matlab™ software. We present numerical results that adequately reproduce the experimental data for the studied temperatures, suggesting that the assumptions on which the model is based on could be valid for this system and can be used to design a PSA cycle to separate CO2/N2 mixtures.